Echoes from a submerged spherical elastic shell coupled to an internal mechanical system

1993 ◽  
Vol 94 (3) ◽  
pp. 1863-1863
Author(s):  
H. Huang ◽  
G. Gaunaurd
Keyword(s):  
Mechanical System ◽  
Elastic Shell ◽  
Spherical Elastic Shell

Scattering of a Plane Acoustic Wave by a Spherical Elastic Shell Near a Free Surface

1995 ◽  
Author(s):  
H. Huang ◽  
G. C. Gaunaurd
Keyword(s):  
Free Surface ◽  
Separation Of Variables ◽  
Mathematical Problem ◽  
Elastic Shell ◽  
Plane Waves ◽  
Spherical Wave ◽  
Acoustic Scattering ◽  
Scattered Wave ◽  
Image Method ◽  
Spherical Elastic Shell

Abstract The acoustic scattering by a submerged spherical elastic shell near a free surface, and insonified by plane waves at arbitrary angles of incidence is analyzed in an exact fashion using the classical separation of variables technique. To satisfy the boundary conditions at the free surface as well as on the surface of the spherical elastic shell, the mathematical problem is formulated using the image method. The scattering wave fields are expanded in terms of the classical modal series of spherical wave functions utilizing the translational addition theorem. Quite similar to the problem of scattering by multiple spheres, the numerical computation of the scattered wave pressure involves the solution of an ill-conditioned complex matrix system the size of which depends on how many terms of the modal series are required for convergence. This in turn depends on the value of the frequency, and the proximity of the spherical elastic shell to the free surface. The ill-conditioned matrix equation is solved using the Gauss-Seidel iteration method and Twersky’s method of successive iteration double checking each other. Backscattered echoes from the spherical elastic shell are extensively calculated and displayed. The result also demonstrates that the large amplitude low frequency resonances of the echoes of the submerged elastic shell shift upward with proximity to the free surface. This can be attributed to the decrease of added mass for the shell vibration.

Elastic-Stress Waves Produced by Pressure Loads on a Spherical Shell

1955 ◽  
Vol 22 (4) ◽  
pp. 473-478
Author(s):  
J. H. Huth ◽  
J. D. Cole
Keyword(s):  
Spherical Shell ◽  
Pressure Wave ◽  
Elastic Stress ◽  
Elastic Shell ◽  
Stress Waves ◽  
Blast Waves ◽  
Constant Speed ◽  
Spherical Elastic Shell ◽  
Technical Interest

Abstract The paper treats the problem of stresses in a spherical elastic shell subjected to a plane pressure wave traveling across it with constant speed, a case of technical interest when considering the effect of blast waves on the structure of a missile in flight.

scholarly journals The shallow shell approach to Pogorelov's problem and the breakdown of ‘mirror buckling’

2016 ◽  
Vol 472 (2187) ◽  
pp. 20150732 ◽  
Author(s):  
Michael Gomez ◽  
Derek E. Moulton ◽  
Dominic Vella
Keyword(s):  
Asymptotic Analysis ◽  
Shallow Shell ◽  
Elastic Shell ◽  
Point Of View ◽  
Stress Profile ◽  
Spherical Cap ◽  
Classic Problem ◽  
Spherical Elastic Shell ◽  
Insight Into ◽  
Energy Formulation

We present a detailed asymptotic analysis of the point indentation of an unpressurized, spherical elastic shell. Previous analyses of this classic problem have assumed that for sufficiently large indentation depths, such a shell deforms by ‘mirror buckling’—a portion of the shell inverts to become a spherical cap with equal but opposite curvature to the undeformed shell. The energy of deformation is then localized in a ridge in which the deformed and undeformed portions of the shell join together, commonly referred to as Pogorelov's ridge. Rather than using an energy formulation, we revisit this problem from the point of view of the shallow shell equations and perform an asymptotic analysis that exploits the largeness of the indentation depth. This reveals first that the stress profile associated with mirror buckling is singular as the indenter is approached. This consequence of point indentation means that mirror buckling must be modified to incorporate the shell's bending stiffness close to the indenter and gives rise to an intricate asymptotic structure with seven different spatial regions. This is in contrast with the three regions (mirror-buckled, ridge and undeformed) that are usually assumed and yields new insight into the large compressive hoop stress that ultimately causes the secondary buckling of the shell.

Sign in / Sign up

Export Citation Format

Share Document